document.write( "Question 166514: For x²(a-b)+a²(b-x)+b²(x-a) show that (x-a) is a linear factor.
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Algebra.Com's Answer #122718 by Edwin McCravy(20081) $\"\"$ $\"About$

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For $\"x%5E2%28a-b%29%2Ba%5E2%28b-x%29%2Bb%5E2%28x-a%29\"$ show that $\"%28x-a%29\"$ is a linear factor.
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document.write( "We use the fact that if a number is substituted for x \r\n" );
document.write( "in a polynomial, the result is the same as the remainder \r\n" );
document.write( "left when that polynomial is divided by x minus that number.\r\n" );
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document.write( "So we substitute  in the polynomial to see if the\r\n" );
document.write( "remainder is 0, and if it is then we'll know that if we \r\n" );
document.write( "had divided the polynomial by , the reaminder\r\n" );
document.write( "would be 0, making  a factor:\r\n" );
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document.write( "So we substitute  into the polynomial:\r\n" );
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document.write( "and everything cancels out and we have\r\n" );
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document.write( "0\r\n" );
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document.write( "so 0 would be the remainder if \r\n" );
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document.write( "were divided by , so \r\n" );
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document.write( " is a factor of  .\r\n" );
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document.write( "And of course  is linear because the highest power\r\n" );
document.write( "of x is 1.\r\n" );
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document.write( "Edwin

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